Abstract

The question of whether people store absolute magnitude
information or relative local comparisons of magnitudes has remained unanswered
despite persistent efforts over the last three decades to resolve it. Absolute
identification is one of the most rigorous experimental benchmarks for evaluating
theories of magnitude representation. We characterize difficulties with both
absolute and relative accounts of magnitude representation and propose an
alternative account that potentially resolves these difficulties. We postulate
that people store neither long-term internal referents for stimuli, not binary
comparisons of size between successive stimuli. Rather, they obtain probabilistic
judgments of size differences between successive stimuli and encode these for
future use, within the course of identification trials. We set up a Bayesian
ideal observer model for the identification task using this representation of
magnitude and propose a memory-sampling based approximation for solving it.
Simulations suggest that the model adequately captures human behavior patterns in
absolute identification.